15-441 Computer Networking

Intra-Domain Routing, Part II

OSPF (Open Shortest Path First)

Lecture #10: 9-27-01 2

A Link-State Routing Algorithm

Dijkstra’s algorithm• net topology, link costs known

to all nodes• accomplished via “link state

broadcast” • all nodes have same info

• computes least cost paths from one node (‘source”) to all other nodes

• gives routing table for that node

• iterative: after k iterations, know least cost path to k dest.’s

Notation:• c(i,j): link cost from node i to j.

cost infinite if not direct neighbors

• D(v): current value of cost of path from source to dest. V

• p(v): predecessor node along path from source to v, that is next v

• N: set of nodes whose least cost path definitively known

Lecture #10: 9-27-01 3

Dijsktra’s Algorithm

1 Initialization: 2 N = {A} 3 for all nodes v 4 if v adjacent to A 5 then D(v) = c(A,v) 6 else D(v) = infinity 7 8 Loop 9 find w not in N such that D(w) is a minimum 10 add w to N 11 update D(v) for all v adjacent to w and not in N: 12 D(v) = min( D(v), D(w) + c(w,v) ) 13 /* new cost to v is either old cost to v or known 14 shortest path cost to w plus cost from w to v */ 15 until all nodes in N

Lecture #10: 9-27-01 4

Dijkstra’s algorithm: example

Step012345

start NA

ADADE

ADEBADEBC

ADEBCF

D(B),p(B)2,A2,A2,A

D(C),p(C)5,A4,D3,E3,E

D(D),p(D)1,A

D(E),p(E)infinity

2,D

D(F),p(F)infinityinfinity

4,E4,E4,E

A

ED

CB

F

2

2

13

1

1

2

53

5

Lecture #10: 9-27-01 5

Link State Characteristics

• With consistent LSDBs*, all nodes compute consistent loop-free paths

• Limited by Dijkstra computation overhead, space requirements

• Can still have transient loops

A

B

C

D

1

3

5 2

1

Packet from CAmay loop around BDCif B knows about failureand C & D do not

X

* Lump Sum Death Benefit? Leisure Studies Data Bank? Latvijas spriedumu datu bâze? >> Link State Data Base

Lecture #10: 9-27-01 6

Dijkstra’s algorithm, discussion

Algorithm complexity: n nodes• each iteration: need to check all nodes, w, not in N• n*(n+1)/2 comparisons: O(n**2)• more efficient implementations possible: O(n log n) (or better)

Oscillations possible:• e.g., link cost = amount of carried traffic

A

D

C

B1 1+e

e0

e

1 1

0 0

A

D

C

B2+e 0

001+e1

A

D

C

B0 2+e

1+e10 0

A

D

C

B2+e 0

e01+e1

initially… recompute

routing… recompute … recompute

amount of flow destined for node A from external source

Lecture #10: 9-27-01 7

Importance of Cost Metric

• Choice of link cost defines traffic load• Low cost = high probability link belongs to SPT and will

attract traffic, which increases cost

• Main problem: convergence• Avoid oscillations• Achieve good network utilization

Lecture #10: 9-27-01 8

Metric Choices

• Static metrics (e.g., hop count)• Good only if links are homogeneous• Definitely not the case in the Internet

• Static metrics do not take into account• Link delay• Link capacity• Link load (hard to measure)

Lecture #10: 9-27-01 9

Original ARPANET Metric

• Cost proportional to queue size• Instantaneous queue length as delay estimator

• Problems• Did not take into account link speed• Poor indicator of expected delay due to rapid

fluctuations• Delay may be longer even if queue size is small due to

contention for other resources

Lecture #10: 9-27-01 10

Metric 2 - Delay Shortest Path Tree

• Delay = (depart time - arrival time) + transmission time + link propagation delay

• (Depart time - arrival time) captures queuing• Transmission time captures link capacity• Link propagation delay captures the physical length of

the link

• Measurements averaged over 10 seconds• Update sent if difference > threshold, or every 50

seconds

Lecture #10: 9-27-01 11

Performance of Metric 2

• Works well for light to moderate load• Static values dominate

• Oscillates under heavy load• Queuing dominates

• Reason: there is no correlation between original and new values of delay after re-routing!

Lecture #10: 9-27-01 12

Specific Problems

• Range is too wide• 9.6 Kbps highly loaded link can appear 127 times

costlier than 56 Kbps lightly loaded link• Can make a 127-hop path look better than 1-hop

• No limit to change between reports• All nodes calculate routes simultaneously

• Triggered by link update

Lecture #10: 9-27-01 13

Consequences

• Low network utilization (50% in example)• Congestion can spread elsewhere• Routes could oscillate between short and long

paths• Large swings lead to frequent route updates

• More messages• Frequent SPT re-calculation

Lecture #10: 9-27-01 14

Revised Link Metric

• Better metric: packet delay = f(queueing, transmission, propagation)

• When lightly loaded, transmission and propagation are good predictors

• When heavily loaded queueing delay is dominant and so transmission and propagation are bad predictors

Lecture #10: 9-27-01 15

Normalized Metric

• If a loaded link looks very bad then everyone will move off of it

• Want some to stay on to load balance and avoid oscillations

• It is still an OK path for some • Hop normalized metric diverts routes that have an

alternate that is not too much longer • Also limited relative values and range of values

advertised gradual change

Lecture #10: 9-27-01 16

OSPF (Open Shortest Path First)

• “open”: publicly available• Uses Link State algorithm

• LS packet dissemination• Topology map at each node• Route computation using Dijkstra’s algorithm

• OSPF advertisement carries one entry per neighbor router

• Advertisements disseminated to entire AS (via flooding)

Lecture #10: 9-27-01 17

OSPF “advanced” features (not in RIP)

• Security: all OSPF messages authenticated (to prevent malicious intrusion); TCP connections used

• Multiple same-cost paths allowed (only one path in RIP)• For each link, multiple cost metrics for different TOS

(e.g., satellite link cost set “low” for best effort; high for real time)

• Integrated uni- and multicast support: • Multicast OSPF (MOSPF) uses same topology data base as

OSPF

• Hierarchical OSPF in large domains.

Lecture #10: 9-27-01 18

Hierarchical OSPF

Lecture #10: 9-27-01 19

Hierarchical OSPF

• Two-level hierarchy: local area, backbone.• Link-state advertisements only in area • each nodes has detailed area topology; only know

direction (shortest path) to nets in other areas.• Area border routers: “summarize” distances to nets in

own area, advertise to other Area Border routers.• Backbone routers: run OSPF; routing limited to

backbone.• Boundary routers: connect to other ASs.

Lecture #10: 9-27-01 20

IGRP (Interior Gateway Routing Protocol)

• CISCO proprietary; successor of RIP (mid 80s)• Distance Vector, like RIP• several cost metrics (delay, bandwidth, reliability, load etc)• uses TCP to exchange routing updates• Loop-free routing via Distributed Updating Alg. (DUAL)

based on diffused computation

Lecture #10: 9-27-01 21

Comparison of LS and DV algorithms

Message complexity• LS: with n nodes, E links,

O(nE) messages• DV: exchange between

neighbors only

Speed of Convergence• LS: O(n log n) algorithm

requires O(nE) msgs• may have oscillations

• DV: convergence time varies• may be routing loops• count-to-infinity problem• (faster with triggered

updates)

Space requirements:• LS maintains entire topology• DV maintains only neighbor

state

Lecture #10: 9-27-01 22

Robustness: what happens if router malfunctions?LS:

• node can advertise incorrect link cost• each node computes only its own table

DV:• DV node can advertise incorrect path cost• each node’s table used by others

• errors propagate thru network

Comparison of LS and DV algorithms

Lecture #10: 9-27-01 23

How To Do Variable Prefix Match

128.2/16

10

16

19128.32/16

128.32.130/24 128.32.150/24

default0/0

0

• Traditional method – Patricia Tree• Arrange route entries into a series of bit tests

• Worst case = 32 bit tests• Problem: memory speed is a bottleneck

Bit to test – 0 = left child,1 = right child

Lecture #10: 9-27-01 24

Speeding up Prefix Match - Alternatives

• Content addressable memory (CAM)• Hardware based route lookup• Input = tag, output = value associated with tag• Requires exact match with tag

• Multiple cycles (1 per prefix searched) with single CAM

• Multiple CAMs (1 per prefix) searched in parallel• Ternary CAM

• 0,1,don’t care values in tag match• Priority (I.e. longest prefix) by order of entries in

CAM

Lecture #10: 9-27-01 25

Speeding up Prefix Match

• Cut prefix tree at 16/24/32 bit depth• Fill in prefix tree entries by creating extra entries

• Entries contain output interface for route• Add special value to indicate that there are deeper tree

entries• Only keep 24/32 bit cuts as needed

• Example cut prefix tree at 16 bit depth • 64K entries!!• Use a variety of clever techniques to compress space

taken

Lecture #10: 9-27-01 26

Prefix Tree

10

1 1 1 5 5 X 7 3 3 3 3 X X 9 51 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Port 1 Port 5 Port 7Port 3

Port 9Port 5

Lecture #10: 9-27-01 27

Prefix Tree

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Subtree 1 Subtree 2

Subtree 3

1 1 1 1 5 5 X 7 3 3 3 3 X X 9 5

Lecture #10: 9-27-01 28

Speeding up Prefix Match

• Scaling issues• How would it handle IPv6

• Other possibilities• Why were the cuts done at 16/24/32 bits?

Lecture #10: 9-27-01 29

Speeding up Prefix Match - Alternatives

• Route caches• Packet trains group of packets belonging to same

flow• Temporal locality• Many packets to same destination

• Other algorithms • Bremler-Barr – Sigcomm 99

• Clue = prefix length matched at previous hop• Why is this useful?